Two parralel chords of dimensions 15.6 cm and 13cm are such that they are on opposite sides of the centre o of a circle and radius 12 cm.calculate the perpendicular distance between the two chords to 2 dp

A perpendicular from the center of a circle to a chord bisects the chord. We can form a right-angled triangle with the radius as the hypotenuse, half the chord length as one leg, and the perpendicular distance from the center to the chord as the other leg.

• Half of chord 1 (c1/2) = 15.6 cm / 2 = 7.8 cm
• Half of chord 2 (c2/2) = 13 cm / 2 = 6.5 cm

• For chord 1 (d1): Radius² = d1² + (c1/2)² 12² = d1² + 7.8² 144 = d1² + 60.84 d1² = 144 - 60.84 d1² = 83.16 d1 = √83.16 ≈ 9.1192 cm

• For chord 2 (d2): Radius² = d2² + (c2/2)² 12² = d2² + 6.5² 144 = d2² + 42.25 d2² = 144 - 42.25 d2² = 101.75 d2 = √101.75 ≈ 10.0871 cm

Since the chords are on opposite sides of the center, the total distance is the sum of their individual distances from the center.
Total distance = d1 + d2
Total distance = 9.1192 cm + 10.0871 cm
Total distance = 19.2063 cm

Total distance ≈ 19.21 cm